Question: Simplify the following expression: $a = \dfrac{7t^2 + 35t - 168}{t + 8} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $7$ , so we can rewrite the expression: $ a =\dfrac{7(t^2 + 5t - 24)}{t + 8} $ Then we factor the remaining polynomial: $t^2 + {5}t {-24} $ ${8} {-3} = {5}$ ${8} \times {-3} = {-24}$ $ (t + {8}) (t {-3}) $ This gives us a factored expression: $\dfrac{7(t + {8}) (t {-3})}{t + 8}$ We can divide the numerator and denominator by $(t - 8)$ on condition that $t \neq -8$ Therefore $a = 7(t - 3); t \neq -8$